Full Idea
It has often been claimed (e.g. by Leibniz) that a single rule governs all syllogistic validity, called 'dictum de omni et null', which says that what is affirmed or denied of any whole is affirmed or denied of any part of that whole.
Gist of Idea
Syllogistic logic has one rule: what is affirmed/denied of wholes is affirmed/denied of their parts
Source
Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 8)
Book Reference
Engelbretsen,G/Sayward,C: 'Philosophical Logic: Intro to Advanced Topics' [Continuum 2011], p.143
A Reaction
This seems to be the rule which is captured by Venn Diagrams.